Exam 7: Rotational Motion and Gravitation

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For any object orbiting the Sun,Kepler's law may be written T2 = kr3.If T is measured in years and r in units of the Earth's distance from the Sun,then k = 1.What,therefore,is the time (in years)for Mars to orbit the Sun if its mean radius from the Sun is 1.5 times the Earth's distance from the Sun?

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A 0.40-kg mass,attached to the end of a 0.75-m string,is whirled around in a circular horizontal path.If the maximum tension that the string can withstand is 450 N,then what maximum speed can the mass have if the string is not to break?

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If a planet has a radius 16.0% greater than that of the Earth but has the same mass as the Earth,what is the acceleration due to gravity at its surface?

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What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

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Calculate the linear speed due to the Earth's rotation for a person at the equator of the Earth.The radius of the Earth is 6.40 × 106 m.

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Two objects are in circular orbits of different radii around the Sun.Which object has the highest orbital speed?

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A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s2 over a 5.0-s interval?

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A spool of thread has an average radius of 1.00 cm.If the spool contains 47.5 m of thread,how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

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If the mass of Venus is 0.786 times that of Earth,and its radius is 0.950 that of Earth,estimate the gravitational acceleration g at the surface of Venus.(gearth = 9.80 m/s2)

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Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed.The direction for the acceleration for this point at that moment is:

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A Ferris wheel starts from rest and builds up to a final angular speed of 1.9 rad/s while rotating through an angular displacement of 4.9 rad.What is its average angular acceleration?

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A satellite is in a circular orbit about the Earth at a distance of d = 5 times the Earth's radius above the surface.What is the speed of the satellite? (The radius of the Earth is 6.4 × 106 m. )

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According to Kepler's second law,Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse.What is at the other focus of the ellipse?

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A point on the rim of a 0.25-m-radius fan blade has centripetal acceleration of 0.20 m/s2.Find the centripetal acceleration of a point 0.05 m from the center of the same wheel.

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A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s2.What is the time interval required for it to reach a 6.50-rad displacement after starting from rest?

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An observation satellite for mapping purposes is placed in a low Earth orbit.In order to see the whole surface of the Earth,which would be the preferred orbit?

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Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 60.0° N latitude.The radius of the Earth is 6.40 × 106 m.

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An asteroid in orbit about the Sun has a linear speed of 4 km/s when at a distance of closest approach d from the Sun.What is its linear speed when it is at its greatest distance from the Sun,a distance 2d?

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Consider a point on a bicycle wheel as the wheel turns about a fixed axis,neither speeding up nor slowing down.Compare the linear and angular accelerations of the point.

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A point on the rim of a 0.15-m-radius rotating disk has a centripetal acceleration of 5.0 m/s2.What is the angular speed of a point 0.075 m from the center of the disk?

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